Quadratic Formula (Cambridge O Level Maths)

How do I use the quadratic formula to solve a quadratic equation?

• A quadratic equation has the form:

  ax² + bx + c = 0 (as long as a ≠ 0)

  • you need "= 0" on one side
• The quadratic formula is a formula that gives both solutions:
  • 

• Read off the values of a, b and c from the equation
• Substitute these into the formula
  • write this line of working in the exam
  • Put brackets around any negative numbers being substituted in
• To solve 2x² - 7x - 3 = 0 using the quadratic formula:
  • a = 2, b = -7 and c = -3
  • 
  • Type this into a calculator or simplify by hand
    • once with + for  ± and once with - for  ±
  • The solutions are x = 3.886 and x = -0.386 (to 3 dp)
    • Rounding is often asked for in the question
    • The calculator also gives these solutions in exact form (surd form), if required
    • x =  and x = 
  • On the non-calculator paper you will be asked to give your answers as simplified surds so make sure that the number under the square root has no square factors
    • If it does then simplify the surd!

What is the discriminant?

• The part of the formula under the square root (b² – 4ac) is called the discriminant
• The sign of this value tells you if there are 0, 1 or 2 solutions
  • If b² – 4ac > 0 (positive)
    • then there are 2 different solutions
  • If b² – 4ac = 0 
    • then there is only 1 solution
    • sometimes called "two repeated solutions"
  • If b² – 4ac < 0 (negative)
    • then there are no solutions
    • If your calculator gives you solutions with i terms in, these are "complex" and not what we are looking for
  • Interestingly, if b² – 4ac is a perfect square number ( 1, 4, 9, 16, …) then the quadratic expression could have been factorised!

Can I use my calculator to solve quadratic equations?

• Yes to check your final answers, but a method must still be shown as above